Odd measures #2: Entourage Depth Index
This Odd Measure was inspired by a quote from Mariah Carey:
I had my team with me but the pups had a mini entourage of their own, of course! And why wouldn’t they? It was a big shoot and even my entourage had an entourage—my stylist had an assistant, my security had extra security [for another version, see this].
Merely having an entourage, of course, is indicative of fame. I’ve never had even the smallest entourage, and I would guess that most academics are below the threshold. Susan Sontag, who I sat next to on a panel once, had a small entourage to sweep her away to the next event. But intellectuals by and large just don’t seem to need them.
Divas, on the other hand, do. Likewise Presidents—the Secret Service is an entourage all by itself. Or Roger Ailes, head of Fox news, who in public is constantly “buffered” by an “elaborate private security detail” paid for by News Corp. I’ll bet that like Mariah Carey’s, his security too has security of its own.
A better measure of your fame and (self-)importance will take account not merely of the size of your entourage, but of its depth. On this basis we would expect the little people—those who have no entourage—to be assigned an index of 0. If you’re like Paula Abdul and all you can muster is a first-order entourage, your index ought to be 1. Mariah Carey’s index, as we’ve seen, will be at least 2.
One complication emerges as we consider the elaborate arrangements around Presidents, Queens, Miss America, Dr. Evil and the like. The collection of entourages around a person, ordered by the “belongs to the immediate entourage of” relation, will be, in favorable cases, a directed tree, that is a directed graph with a designated node such that between that node and any other node there is exactly one path. In the graph of entourages all paths lead to the Star.
Take the tree at right (all edges are understood to be directed upwards). The longest paths contain three entourages, but there are also paths containing only two. How, then, should the ENTOURAGE DEPTH INDEX be defined?
An important person has a large entourage, of course, but also, one would think, a deep one. Largeness corresponds to breadth, to the average number of nodes at each level; overall depth to some measure where we give greater weight to nodes that are farther away from the top. (If you set the EDI simply to the length of the longest path, then you’re ignoring breadth altogether.) I’m not sure there is a universal measure: after all, in some contexts, breadth would indicate importance better than depth, and in others vice versa. Criminal organizations tend toward flatness, armies toward depth.
The examples mentioned above suggest another index, the SDI or Security Depth Index. But I suspect that, as the story about Roger Ailes shows, the SDI would not be a measure of importance so much as of paranoia.
